Quasifinite representations of W_∞

1999/10/29 by Victor G. Kač, Victor G. Kac, Kac, Victor G. +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/9910172

Amstex, 18 pages

arxiv created 1999/10/29 · openalex publication_date 1999/10/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the quasifinite highest weight modules over a family of subalgebras W_∞ⁿ of the central extension W_1+∞ of the Lie algebra of differential operators on the circle consisting of operators of order ≥ n. We classify the unitary quasifinite highest weight modules over W_∞=W_∞¹ and realize them in terms of unitary highest weight representations of the Lie algebra of infinite matrices with finitely many non-zero diagonals.

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